A wide variety of closures for doors, luggage, chests and the like have been proposed, most of which involve latching at one point. To provide the greatest measure of security combined with the strength of the material used in the structure to be closed, it would be desirable to have a peripheral closing system that locked or fastened at more than one point around the perimeter of the aperture being closed, while retaining the convenience of one operating latch. However, previous multiple peripheral closures have been complex, and unacceptable for applications such as luggage in which weight is an important consideration.